On Thursday, August 18, 2011 08:19:13 am G Y wrote:
> Dear all,
>
> I am a student in crystallography. So not quite familiar with some even
> basic concepts.
>
> In shelx .hkl file or ccp4 .mtz file there is a column SIGF which is related
> to standard deviation of the structure factor. I read through many text book
> for crystallography, there are many formulas about this topic. Sometimes it
> is a square of sigma, sometimes it is not.
>
> My question is:
>
> 1. What is the exact mathematical formula for SIGF or SIGFP in ccp4 or shelx
> format file?
There is none. The column in the file simply holds whatever value was
input from some data-processing program. You need to take a step back
and ask how each individual program calculates, or estimates, sigma(F).
>
> 2. If it can be calculated from F, why it is necessary to include it in ccp4
> or shelx reflection file (they have F already) ?
It cannot be calculated from F.
> 3. Is this value really important in structure determination? Why and how?
> As I understood, during data collection each reflection measured several
> times, so there is a deviation from the average F. That is the meaning of
> SIGF. But how to use this value in structure determination? Is there some
> kind of correction or refinement on F according to SIGF?
It tells you how much faith to put in that particular Fobs.
If the sigma value is small (compared to Fobs) then you would tend to have
confidence that the Fobs value is accurate, and therefore rate your current
model better if it correctly predicts Fobs. Conversely, if the sigma value
is large then you would tend to think that Fobs is unreliable and therefore
not penalize your current model if Fcalc != Fobs.
This line of reasoning explains why the primary use of sigma is to weight
the various residuals during refinement. Typically the weight assigned
to each observation is (1 / sigma^2).
Although it goes a step or two beyond the specific question you asked,
I suggest that you work through Randy Read's notes on maximum likelihood,
weighting, and least-squares.
http://www-structmed.cimr.cam.ac.uk/Course/Likelihood/likelihood.html
This may lead to a deeper understanding of how accounting for sigma
leads to a better model.
Ethan
> And also when multiplicity during data collection is low, the SIGF would not
> be so interested. So is that means the SIGF would not be so important in
> some measurements?
>
> Any kind reply from you guys would be greatly appreciated. Many thanks!
>
> Best regards,
> G
>
--
Ethan A Merritt
Biomolecular Structure Center, K-428 Health Sciences Bldg
University of Washington, Seattle 98195-7742
